Question

Given that ABCD is a rhombus, what is the value of x?​

Answer 1

Option D

Explanation:

In any Rhombus the diagonals bisect the angles. The diagonals are perpendicular bisectors of each other.

So,

5x-18+x+90=180 ( Angles of a triangle add to 180 degrees)

Simplifying like terms:

6x+72=180

Subtracting 72 both sides :

6x= 108

Dividing by 6 both sides:

x=18.

Option D is correct.

Answer 2

D. 18

Explanation:

We know:

1. Diagonals of a rhombus are perpendicular.

2. Diagonals divide the rhombus on four congruent right triangles.

3. The sum of measures of acute angles in a right triangle is equal 90°.

Angles CAD and ACB are alternate angles. Therefore they are congruent:

m∠DAC = m∠ACB ⇒ m∠ACB = x°.

From 3. we have the equation:

(5x - 18) + x = 90

(5x + x) - 18 = 90 add 18 to both sides

6x = 108 divide both sides by 6

x = 18